dynamically adaptive numerical methods have been developed to find solutions for differential equations. thesubject of wavelet has attracted the interest of many researchers, especially, in finding efficient solutions fordifferential equations. wavelets have the ability to show functions at different levels of resolution. in this paper, a numerical method is proposed for solving the second pain...

We propose a new modification to Adomian decomposition method for numerical treatment of the time-dependent EmdenFowler-types equations with the Neumann and Dirichlet boundary conditions. In new modified method, we use all the boundary conditions to derive an integral equation before establishing the recursive scheme. The new modified decomposition method (MDM) will be used without unknown cons...

in this work, the solution of a boundary value problem is discussed via asemi analytical method. the purpose of the present paper is to inspect theapplication of the adomian decomposition method for solving the nagumo tele-graph equation. the numerical solution is obtained for some special cases sothat demonstrate the validity of method.

first riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. an analytical approximation of the solution of nonlinear differential riccati equation is investigated using the adomian decomposition method. an application in optimal control is presented. the solution in different order of approximations and different methods of approximat...

In this paper, the Adomian decomposition method for the approximate solution of generalized Korteweg de Vries equation with boundary conditions is implemented. By using this method, the solution is calculated in the form of power series. The method does not need linearization, weak nonlinearity or perturbation theory. By using Mathematica Program, Adomian polynomials of the obtained series solu...

We prove convergence of the Adomian decomposition method for an abstract initial-value problem using the method of majorants from the Cauchy-Kowalevskaya theorem for differential equations with analytic vector fields. Convergence rates of the Adomian method are investigated in the context of the nonlinear Schrödinger equation. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq...

In this paper, a modified nonlinear Schrödinger equation with spatiotemporal dispersion is formulated in the senses of Caputo fractional derivative and conformable derivative. A new generalized double Laplace transform coupled Adomian decomposition method has been defined applied to solve newly dispersion. The approximate analytical solutions are obtained compared each other graphically.

In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having four different solutions to illustrate the efficiency of the proposed method under strongly generalized differentiability. Keywords—Fuzzy-valued function, Fuzzy initial value...

Abstract: Convergence of Adomian decomposition method (ADM) is ofa great importance when applied to different types of linear and nonlinear equations.In this paper, a general proof of convergence of ADM is introduced. In this work, a reliable approach for convergence of the Adomian method is discussed. Convergence analysis is reliable enough to estimate the maximum absolute truncated error of t...